I have a 24’x24′ basement that the previous homeowner finished with 1/2″ drywall over 2×4 wood studs without vapor barrier or insulation.  The stud wall is held away from the concrete block basement walls 1/4″ – 1/2″.  Sill plate is not treated wood.  We are not living in the house right now because we are in the middle of an entire home remodel.  It’s been very humid here in the midwest the past couple of weeks and we got some surface mildew growth on the lower 12 inches of the drywall around the perimeter of the room.  We noticed it within a day or two, cleaned it off with bleach/water and set up a humidifier and fans to keep the air circulating.  We also removed a section of drywall 24 inches up from the floor to see if we had further problems behind the drywall.  Although the bottom 24 inches or so of the block was damp, the woods studs looked fine and the back of the drywall we removed was clean too (no mold).  Since we added the fans and dehumidifier the exposed block is now dry.  My question is should I put back the drywall and move on or should I remove the drywall and wood studs and start over by adhering rigid foam to the block walls before building the stud walls?  This space will be air conditioned/heated year around.  My other thought was to install transfer grilles every so often along the bottom and top of the walls to encourage air circulation behind with the stud cavity.  Any thoughts/ideas would be appreciated.